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Search: id:A135337
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| A135337 |
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Number of Dyck paths of semilength n with no DUUU's starting at level 1. |
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+0
2
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| 1, 1, 2, 5, 13, 36, 105, 320, 1011, 3289, 10957, 37216, 128435, 449142, 1588228, 5669505, 20403322, 73945553, 269647630, 988642372, 3642310793, 13476857235, 50059454347, 186598634398, 697777187275, 2616919372356, 9840647362248
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Column 0 of A135331. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 14 2007
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REFERENCES
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A. Sapounakis, I. Tasoulas and P. Tsikouras, Counting strings in Dyck paths, Discrete Math., 307 (2007), 2909-2924.
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FORMULA
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G.f.=1+zC^2/(1+z^3*C^4)=(1-z)(2C-1)/[(1-2z)C+z], where C=[1-sqrt(1-4z)]/(2z) is the g.f. of the Catalan numbers (A000108). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 14 2007
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EXAMPLE
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a(4)=13 because among the 14 (=A000108(4)) Dyck paths of semilength 14 only UDUUUDDD does not qualify.
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MAPLE
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G:=(2*C-1)/(C-z*(2*C-1)): C:=((1-sqrt(1-4*z))*1/2)/z: Gser:=series(G, z=0, 30): seq(coeff(Gser, z, n), n=0..27); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 14 2007
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CROSSREFS
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Cf. A000108, A135331.
Sequence in context: A125094 A114465 A135310 this_sequence A133365 A135335 A066723
Adjacent sequences: A135334 A135335 A135336 this_sequence A135338 A135339 A135340
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Dec 07 2007
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 14 2007
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